It is on top of all windows and can not be completely closed. I can move it or hide it my clicking an empty space on the tile bar at the bottom. I have no idea what it's trying to tell me. Something important I'm sure. 
Hi Dan.
Please do not worry, we'll certainly help you resolve it.
Could you share a screenshot (http://avgclick.me/getscreenshot) of the box?
An AVG message box keeps popping up but it is totally black (the colour). It can't be closed or minimized!
Why is this happening and how can it be fixed?
it IS apparently the control panel window. It pops up when the system icons on the lower right is clicked or I select AVG Internet Security from the start menu.
Thank you for the screenshot Dan.
We request you to repair the AVG program from the control panel, since you're getting the black screen.
Refer this article for the repairing the program https://support.avg.com/SupportArticleView?urlname=Repair-AVG-Antivirus
Once you repaired the program, please check for the issue again.
Keep us posted.
Hi Dan.
Please do not worry, we'll certainly help you resolve it.
Could you share a screenshot (http://avgclick.me/getscreenshot) of the box?
Thank you for trying, Dan.
I have sent an email with the steps to uninstall AVG Internet Security and install it again
Please check the email and follow the steps and monitor if you see the same screen again.
It is on top of all windows and can not be completely closed. I can move it or hide it my clicking an empty space on the tile bar at the bottom. I have no idea what it's trying to tell me. Something important I'm sure.